Defects and multistability in eutectic solidification patterns

We use three-dimensional phase-field simulations to investigate the dynamics of the two-phase composite patterns formed upon during solidification of eutectic alloys. Besides the spatially periodic lamellar and rod patterns that have been widely studied, we find that there is a large number of additional steady-state patterns which exhibit stable defects. The defect density can be so high that the pattern is completely disordered, and that the distinction between lamellar and rod patterns is blurred. As a consequence, the transition from lamellae to rods is not sharp, but extends over a finite range of compositions and exhibits strong hysteresis. Our findings are in good agreement with experiments.Comment: 6 pages, 8 figure

Pattern formation in inclined layer convection

We report experiments on thermally driven convection in an inclined layer of large aspect ratio in a fluid of Prandtl number $\sigma \approx 1$. We observed a number of new nonlinear, mostly spatio-temporally chaotic, states. At small angles of inclination we found longitudinal rolls, subharmonic oscillations, Busse oscillations, undulation chaos, and crawling rolls. At larger angles, in the vicinity of the transition from buoyancy- to shear-driven instability, we observed drifting transverse rolls, localized bursts, and drifting bimodals. For angles past vertical, when heated from above, we found drifting transverse rolls and switching diamond panes.Comment: For MPEG movies, see http://milou.msc.cornell.edu/ILCmovie

Lattice Boltzmann simulations of 3D crystal growth: Numerical schemes for a phase-field model with anti-trapping current

A lattice-Boltzmann (LB) scheme, based on the Bhatnagar-Gross-Krook (BGK) collision rules is developed for a phase-field model of alloy solidification in order to simulate the growth of dendrites. The solidification of a binary alloy is considered, taking into account diffusive transport of heat and solute, as well as the anisotropy of the solid-liquid interfacial free energy. The anisotropic terms in the phase-field evolution equation, the phenomenological anti-trapping current (introduced in the solute evolution equation to avoid spurious solute trapping), and the variation of the solute diffusion coefficient between phases, make it necessary to modify the equilibrium distribution functions of the LB scheme with respect to the one used in the standard method for the solution of advection-diffusion equations. The effects of grid anisotropy are removed by using the lattices D3Q15 and D3Q19 instead of D3Q7. The method is validated by direct comparison of the simulation results with a numerical code that uses the finite-difference method. Simulations are also carried out for two different anisotropy functions in order to demonstrate the capability of the method to generate various crystal shapes

Effects of CP-violating phases in supersymmetry

Recent studies about the impact of the CP-violating complex parameters in supersymmetry on the decays of third generation squarks and about T-odd asymmetries in neutralino and chargino production and decay are reviewed. The CP-even branching ratios of the third generation squarks show a pronounced dependence on the phases of A_t, A_b, mu and M_1 in a large region of the supersymmetric parameter space. This could have important implications for stop and sbottom searches and the MSSM parameter determination in future collider experiments. We have estimated the expected accuracy in the determination of the parameters by global fits of measured masses, decay branching ratios and production cross sections. We have found that the parameter A_t can be determined with an error of 2 - 3%, whereas the error on A_b is likely to be of the order of 50 - 100%. In addition we have studied CP-odd observables, like asymmetries based on triple product correlations, which are necessary to unambiguously establish CP violation. We have analysed these asymmetries in neutralino and chargino production with subsequent three-body decays at the International Linear Collider with longitudinally polarised beams in the MSSM with complex parameters M_1 and mu. The asymmetries, which appear already at tree-level because of spin correlation between production and decay, can be as large as 20% and will therefore be an important tool for the search for CP-violating effects in supersymmetry.Comment: 13 pages, LaTeX, 7 eps figures, uses appolb.cls, presented at the final meeting of the European Network ``Physics at Colliders'', Montpellier, September 26 - 27, 200

Percolation-dependent Reaction Rates in the Etching of Disordered Solids

A prototype statistical model for the etching of a random solid is investigated in order to assess the influence of disorder and temperature on the dissolution kinetics. At low temperature, the kinetics is dominated by percolation phenomena, and the percolation threshold determines the global reaction time. At high temperature, the fluctuations of the reaction rate are Gaussian, whereas at low temperature they exhibit a power law tail due to chemical avalanches. This is an example where microscopic disorder directly induces non-classical chemical kinetics.Comment: Revtex, 4 pages, 5 figure

Remarks on some open problems in phase-field modelling of solidification

International audienceThree different topics in phase-field modelling of solidification are discussed, with particular emphasis on the limitations of the currently available modelling approaches. First, thin-interface limits of two-sided phase-field models are examined, and it is shown that the antitrapping current is in general not sufficient to remove all thin-interface effects. Second, orientation-field models for polycrystalline solidification are analyzed, and it is shown that the standard relaxational equation of motion for the orientation field is incorrect in coherent polycrystalline matter. Third, it is pointed out that the standard procedure of incorporating fluctuations into the phase-field approach cannot be used in a straightforward way for a quantitative description of nucleation